Log Definition and 632 Threads

In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Monomials – relationships of the form



y
=
a

x

k




{\displaystyle y=ax^{k}}
– appear as straight lines in a log–log graph, with the power term corresponding to the slope, and the constant term corresponding to the intercept of the line. Thus these graphs are very useful for recognizing these relationships and estimating parameters. Any base can be used for the logarithm, though most commonly base 10 (common logs) are used.

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  1. QuarkCharmer

    Log equation with two raised variables

    Homework Statement This is not a specific problem that I must complete, but I realized that I forgot how to solve these style problems! Homework Equations The Attempt at a Solution For instance, off the top of my head: 3e^{x+1}=e^{x+2} I would divide both sides through by 5 to get...
  2. J

    Solve the equation log (little 3) X + log (little6) X = 2

    Solve the equation log (little 3) X + log (little6) X = 2 the answer is 3.9 Here is what I try log (little 6)x = log (little 3)x/log (little 3)6 = log (little 3) (x-6)log (little 3)x + log (little 3) (x-6) = 2 log (little3) (x(x-6)) =2 log (little3) (x^2-6x)=3^2 x^2 -6x =9 x^2-6x-9=0 x= 7.2...
  3. D

    Difficult partial derivative of a log

    Hello! I am trying to solve the partial derivative 'P' http://www.flickr.com/photos/61865210@N07/5757168138/ , which is part of a larger equation: http://www.flickr.com/photos/61865210@N07/5757300018/ (Sorry, can't seem to display to pictures, using insert image) Someone told me that solving...
  4. Saitama

    Identities for solving log questions

    I was wondering if there could be more identities than i have read. I was doing questions on log and found many questions in this form:- (loga b)2 (loga b)(loga c) This is not my homework but i require these identities to solve the questions. Please someone tell me how to solve these...
  5. Hepth

    Mathematica Mathematica : Log Handling/Simplification

    I'm having a simple problem with simplifying of logs. Given the input : FullSimplify[8 Log[m1] - 8 Log[m2] + 4, m1 > 0 && m2 > 0] FullSimplify[8 Log[m1] - 8 Log[m2], m1 > 0 && m2 > 0] I get out: 8 log(m1)-8 log(m2)+4 8 log(m1/m2) So for the second command it combines the logs...
  6. E

    Solving Exponential Equations: 2 Problems with Multiple Solutions

    Homework Statement it wants the sum of all solutions 2 different problems 1. and 2. 1. 2^x + 2^(x+1) + 2^(x+2) = 2^6. 2. 8/(3^x +2)>=3^x >= meaning equal or greater than 3^x Homework Equations should i come up with a summa equation? The Attempt at a Solution i...
  7. E

    Solving Logarithmic Equation with Real Numbers: Log Problem Homework

    Homework Statement 9^x-5*3^X+6=0 Homework Equations I have no idea how to solve this i suspect there is a theory that I am not familiar with involved. want real numbers. The Attempt at a Solution i thought about moving the 6 to the otherside and doing log on both but you can't...
  8. P

    Trouble with Log Laws and exponential functions

    Please help i have these two questions and i am Stuck! Question 1 The linear equation you have found (y=.771x+1.609) is in the form of y= mx +c. it should be however more appropreiatly be considered as being in the form, lny = mx + lnA. by using appropriat logarithmic and exponential laws...
  9. S

    Log Fume Acceleration, Velocity, and change in mass

    Currently working on a high school physics assignment. I need help on some questions, just so that I know I am in the right direction. I am not here to get you guys to do my homework for me. But anyway, the following questions are about a log fume ride, and the acceleration and velocity of a...
  10. Y

    Solve Log Problem: Integral of (1/x) from -b to -a with Formula ln(x)

    \int_{-b}^{-a} \frac{dx}{x} = ln(x)|_{-b}^{-a} What is this equal to? I don't know how to proceed. Please help. Thank Alan
  11. C

    Integration results in natural log of a natural log

    SORRY FOR THE LACK OF FORMATTING, I SPENT 30 MINUTES TRYING TO FORMAT AND IT KEPT GETTING MESSED UP. Homework Statement Evaluate by substitution. Integral of dx/xln(x^2) Homework Equations integral of 1/u du = ln(u) + C The Attempt at a Solution u = ln(x^2) du = 2/x...
  12. S

    Derivative Problem involving Natural Log

    Homework Statement Evaluate the derivative of the following function: p(x) = (5x)-ln(5x) Homework Equations \frac{d}{dx}lnx = \frac{1}{x} Not sure what else... The Attempt at a Solution I know that I will have to use the chain rule in this problem, but actually...
  13. M

    Log amp cascaded to anti-log amp

    Hey everybody, I've been trying a bit of an experiment involving cascading an inverting logarithmic amp with an inverting exponential amplifier. Between them I put in an inverting buffer (see attached diagram). Now the thing is, when the inverting buffer has unity gain everything works as...
  14. K

    What is the area under the given equation using definite integration?

    Homework Statement Find the area under the given equation using definite integration. y = 4ln(3-x) from 0 to 2 The Attempt at a Solution Integration from 0 to 2 4 (integration from 0 to 2) (3-x) Let u = 3-x du = -dx -du = dx -4(integration from 0 to 2) du Idk where to go from there :/...
  15. W

    Looking for descriptive material about log inequalities.

    So, I have this book that doesn't explain why you have to first find the domain, consolidate logs, solve the function as a rational inequality, find the key numbers, then find which numbers of the key numbers are actually in the domain according to the inequality, and finally write out the...
  16. M

    Reverce log, Anti-log, or unlog whitch is correct?

    Title pretty much says it, is there an offical opinion that can be quoted somewhere to win a bet? I like unlog or Reverse log but Anti-log just sounds goofy.
  17. V

    Error analysis in log space: How to handle exponents in regression analysis?

    Homework Statement Maybe, I am a little stupid, but I just can't understand what I am doing wrong here. I have 2 quantities which I have to convert to log (base 10) and perform a regression analysis. Quantity=1.235e9 error=3.4475e8 Homework Equations I have to express the above...
  18. J

    Which Graph Paper to Use for Power Relationships: Semi-Log vs Log-Log?

    After collecting data from an experiment and realizing that there is a power relationship, how do u know if u need to use semi log graph paper or log-log paper to graph your data?
  19. N

    Comparing log(i^2) and 2*log(i)

    Homework Statement Show log(i^2) and 2*log(i) have different sets of values. Homework Equations log z=ln|z|+i*arg z The Attempt at a Solution log(i^2) = ln|i^2| + i*arg(i^2) = ln|-1| + i*(pi + 2*n*pi) = 0 + i*pi*(1 + 2*n) =...
  20. T

    How to Solve Logarithmic Equations Using Change of Base Formula?

    1) logba + logcb + logac = 1/logab + 1/logbc + 1/logca 2) logrp = q and logqr = p, show logqp = pq 3) if u = log9x, find in terms of u, logx81 4) log5x = 16logx5, solve for x attempt I know the change of base formula logax = logbx/logba, but I'm not sure if/how to apply it in any...
  21. N

    Exploring the Complex Logarithm Function for Different Branches

    Homework Statement Show that (a) log(i^2) = 2*log(i) when log z=ln r + i * theta (r>0 and pi/4 < theta < 9*pi/4) (b) log(i^2) <> 2*log(i) when log z=ln r + i * theta (r>0 and 3*pi/4 < theta < 11*pi/4) Homework Equations log z = ln r + i * theta The Attempt at a Solution Got...
  22. E

    Natural Log in Thermodynamic Equations related to Entropy.

    Well I've been doing fairly complex thermodynamics in classical mechanics lectures with a bit of medium to advanced class, first of all , it took me a very long time to wrap my head around the concept of Entropy, however I still don't understand why we use ln (Natural Log) to calculate the...
  23. I

    This should be easy Units of log graph?

    I have a question that sounds easy but as of yet no one has been able to give me a satisfactory explanation. I made a plot of mobility (cm^2/Vs) against temperature (K), i then wanted to find an expression that showed the relationship between the two. What i did was took the natural logarithm of...
  24. H

    Another another more challenging log question.

    another another more challenging log question. :( Homework Statement log6(5y − 5) = 4x^2 + 7 Homework Equations - The Attempt at a Solution 6( x^2 + 6x+5 ) +1
  25. T

    Derivative of Log Function: Is My Solution Correct?

    Homework Statement y=ln (-2+√x)/(x^4) Hi there. Just need some reassurance that I found the derivative of this equation correctly. Also, if you can give me feedback on typing my equations that would also be wonderful. (Whether or not there are easier/better ways of typing the equations.)...
  26. A

    Solve a = b^(logx), for x: Steps & Explanation

    I can't seem to remember how you solve a = b^(logx), for x. What are the steps for simplifying this again?
  27. M

    Log Question - Relationship between two points on log function

    Hi Physics Forums, I understand that I usually need to show that I've attempted a question in order to get feedback, but I have absolutely no idea how to approach this one Calculus Log question. Base = 10 log (2) = 0.301103, log (3) = 0.47715 a.) Find log base 6 (5) b.) Estimate...
  28. K

    Integration of natural log problem

    Homework Statement what is the integral of ln(e2x-1) dx 2. The attempt at a solution I got u= ln(e2x-1) du = 2e2x-1 \ e2x-1 du = 2 dx 1/2(integral of u du) 1/2 ln (e2x-1 ) +c = 1/4 [ln (e2x-1 )]2 + c Could you please let me know if this is correct? I don't know how to integrate ln...
  29. M

    Solve Natural Log Equation: ln(x+1)-ln(x)=0

    Homework Statement Given the Equation ln(x+1)-ln(x)=0 find x (If it exists. Homework Equations The Attempt at a Solution ln(x+1)-ln(x)=0 ln(x+1)=ln(x) x+1 = x 1 = x-x Solution does not exist. (My book "agrees" with me in the solutions.) However, typing up the...
  30. Kawakaze

    Range of natural log, some trigonometry

    Homework Statement (1) Real variables x and y are related by the equation 3ln(y +4) = 2ln(x +2) − 2ln(x +9)+3ln(x^2 − 1). Determine the range of values of x and y for which the expressions on each side of this equation are defined. Find y explicitly as a function of x, that is...
  31. U

    How can Stirling's approximations be used to simplify a log equation?

    This is from a worked example involving using Stirlings approximations. I have the log equation, where c<<1: S=K(Nln(N)-cNln(cN)-N(1-c)ln(1-c)) In the next line of the example, this is simplified to S=-kNcln(c) I've tried a few ways of getting to this, but have had no...
  32. H

    Whats the point log mean temp difference(LMTD) any why use it?

    I have a solution to a problem but don't understand why to use LMTD vs the usual type of mean. I was working on a problem of trying to find the thermal resistance through a coaxial cable(hollow cylinder) and sort of knew the trick was that the area was not constant thus something had to be...
  33. Z

    Infinite series converging to natural log

    Prove that sum 1/2^(n+1)*n/(n+1), from n=0 to infinity, converges to 1 - log(2), where log stands for the natural logarithm. I know that the Taylor series for log(x) about x=1 is sum (-1)^(n+1)*(x-1)^n/n, but I don't see how these two statements are consistent. Thanks for any pointers!
  34. T

    Proving Log Relationship: x2 + y2 = 11xy and log [(x-y)/3] = 0.5(logx + logy)

    Given that x2 + y2 = 11xy Show that log [ (x-y)/3 ] = 0.5 (logx +logy) Similarly, Give that log [ (x-y)/3 ] = 0.5 (logx +logy) Show that x2 + y2 = 11xy I really liked the log unit and understood it, but I was stumped on this question. It was for a test and it keeps bothering me...
  35. T

    How do you solve log equations?

    Homework Statement Solve: a) b) 3log (x-15) = (1/4)x The Attempt at a Solution For a) http://i1141.photobucket.com/albums/n596/physics-/43_6051b53e5bf48508fa9854606102060a.png http://i1141.photobucket.com/albums/n596/physics-/46_ab0ccd938c1710d9cb5bbcd6193d4eac.png...
  36. T

    Why Do These Log Equations Have No Solutions?

    Homework Statement In the answers, it says these two don't have any solutions. I don't understand how, though. log(v-2) = 1 +log(v+2) and 2 + logx = log(x-9) The Attempt at a Solution For the first one, I did: log(v-2/v+2) = 1 v-2/v+2 = 10 v-2 = 10v + 20 0 = 9v + 22 So I didn't...
  37. T

    Calculating Population Growth Rate Using Log Equations

    Homework Statement Equation for population growth is: P(t) = P0(1 + R/100)t/t0 R --- growth rate in % t0--- time period Suppose a population grew from 10 000 to 25 000 in 6 years. If time is measured in years, calculate: a)Yearly growth rate Answer:16.5% b) Growth rate per decade...
  38. M

    Double Integral Plus Integration by Parts with Natural Log Problem

    Homework Statement My homework problem is the double integral of y/1+xy dxdy. It is a definite double integral and both integrands have the values of a = 0 and b = 1. Homework Equations Integration by parts: uv - int(vdu) The Attempt at a Solution My first step of the double integral is I...
  39. QuarkCharmer

    Log Explanations for Homework Statement - Inflation & Property Value

    Homework Statement During a 10 year period of constant inflation, the value of a $200,000 property will increase according to the equation v = 200,000e^(.06t). a.) What will be the value of the property in 4 years? b.) Use a table/graph to estimate when this property will double in value...
  40. T

    Solve LOG Problem: Evaluate Log 3 (Base 27) Without Calculator

    1. Evaluate WITHOUT using a calculator. 2. log base 27, 3, that is, log 3 with a base of 27 instead of 10 3. I'm stuck on how you end up with the solution, which is 1/3. Can someone provide a step by step walk through on how to solve this problem without a calculator?
  41. T

    Units into Log and Exponential Functions

    Hello, Something I've wondered about for some time is what happens to units once we pump them into a exponential or log function. For example in neutron attenuation I(x) = I_0 * exp(-Sigma * x) I feel like this something I should know, but I just don't get it. I suspect what's...
  42. T

    Jump Over Log with Least Effort: Analyzing Velocity vs Angle

    1.A lazy flea approaches a stationary log with radius R. At what distance from the log must the flea be to jump over the log with the least amount of effort. Hint: Plot Velocity versus the angle. 2.(Not sure how I should type these) I plan to use constant acceleration projectile motion...
  43. A

    What am i doing wrong? Log differentiation

    Homework Statement Use logarithmic differentiation to find the derivative of the function. y=xln(x) also, if anyone could help me with this... i have (for a diff problem) 1/(x2-1)1/2 * 1/2(x2-1)-1/2*2x i know that is right, but i don't know how to get from that, to x/(x2-1) i keep...
  44. A

    How to Use Logarithmic Differentiation in Calculus

    Homework Statement Hi again Practicing log differentiation now :P Sorry for all the questions, i have a midterm on thursday and i need to get this stuff by then 1. ex2ln(2x+1) 2.ln(2x/(2x+1)) 3. (3x-2)x (use logarithmic differentiation even though unnecessary The Attempt at a Solution 1...
  45. A

    Am i right? solving log functions

    Am i right? :) solving log functions! Homework Statement solve the following equations 1. e4x=25 2. ln(x2-8x+13)=0 The Attempt at a Solution 1. lne4x=ln25 => 4x=ln25 => x=(1/4)ln25 x=0.8047 2. ln(x2-8x+13)=0 => e0=x2-8x+13 => 1= x2-8x+13 => x2-8x+12=0 (x-6)(x-2)...
  46. E

    Common log question (are you done?)

    the rule states, log x => log 10^x the problem said to evaluate / solve and show work. so: log 1000 = log 10 ^ 1000. I'm I done at that point or do I have to go on and solve it? log 10^1000 = x 10 ^ x = 1000 x = 3 which one goes? do I leave it as log 10 ^ 100 or because the problem...
  47. P

    What is the connection between Arctanh x and the logarithmic function?

    I can not seem to figure out why Arctanh x [ Hyperbolic Arctan ] can be expressed as Arctanh x = (1/2) [ Log (1+x) - Log (1-x) ] Note; I know the 1/2 means the expression is a square root of the ratio of the 2 binomials and has been taken out with the Power Rule Can anyone show me the...
  48. S

    Power series expansion for Log z

    Homework Statement Find the power series expansion of Log z about the point z = i-2. Show that the radius of convergence of the series is R = \sqrt{5}. Homework Equations None The Attempt at a Solution I know that Log z = (z-1) - (1/2)(z-1)^2 + (1/3)(z-1)^3 -... So wouldn't this...
  49. S

    Big Oh: showing that a polynomial grows faster than any log function.

    Big Oh: showing that a polynomial "grows faster" than any log function. Homework Statement is n^0.01 big oh of (log(n))^10 ? ***Bear in mind, the log is a binary log. Homework Equations the formal statement would be... does n^0.01 < c(log(n))^10 hold for all n greater than a...
  50. B

    Help with natural log in this equation

    So I am not quite sure how to solve for x here. 1.2E-21=(.3567)(ln(x/.175))
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